A080435 - OEIS

%I #14 May 16 2020 08:55:36

%S 1,2,3,5,7,8,13,14,19,20,23,25,27,31,37,43,47,49,50,55,57,61,67,73,75,

%T 79,85,91,97,98,103,107,109,111,115,121,127,131,133,135,139,140,145,

%U 151,157,163,169,175,181,185,187,193,199,200,205,211,212,217,223,229

%N a(1) = 1; a(n) = least k > a(n-1) such that each prime of form a(i)+a(j) occurs for unique i <= j.

%C Conjecture: There are infinitely many primes not of the form a(i)+a(j). - _David W. Wilson_, Apr 14 2003

%C Are there infinitely many even numbers in the sequence? - _David W. Wilson_, Apr 14 2003

%H Jinyuan Wang, <a href="/A080435/b080435.txt">Table of n, a(n) for n = 1..1000</a>

%t a[1]=1; p[1]={2}; a[n_] := Module[{k, new}, For[k=a[n-1]+1, Intersection[p[n-1], (new=Select[(a/@Range[n-1])+k, PrimeQ])]!={}, k++, Null]; p[n]=Union[p[n-1], new]; a[n]=k];

%o (PARI) v=vector(1000); print1(v[1]=1, ", "); vv=vector(1000); vv[1]=1; n=1; while(n<100, n=n+1; for(m=1, 10^9, f=0; if(!vv[m], v[n]=m; w=vector(1000); for(k=2, n, for(l=1, k-1, s=v[k]+v[l]; if(isprime(s), if(w[s], f=1; break, w[s]=1))); if(f, break)); if(!f, print1(m, ", "); vv[m]=1; break))))

%Y A082929 lists primes not of the form a(i)+a(j). A082930 lists even terms. Cf. A082931.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Feb 20 2003

%E Corrected and extended by _Ralf Stephan_, Apr 14 2003